The Welsh striker does not figure in the plans of City manager Roberto Mancini and Celtic boss Neil Lennon is interested in bringing him in.
Lennon admitted over the weekend it could be a deal that is not sorted out one way or the other until the final day of the transfer window, but Lawwell says they would not be able to afford his wages.
He is not ruling out a loan swoop, though, insisting an agreement might be reached with Bellamy and City's help.
"We've gone for high-profile loan signings in the past few years but some of them have been opportunistic," Lawwell said in the Daily Record.
"We have been in a position to do deals and sometimes the circumstances are right just as the transfer window is beginning to close. But as things stand at the moment we wouldn't be able to do a deal with Craig Bellamy.
"I know Neil would love to have him at the club - we all would - but we cannot pay salaries of ?70,000-?80,000. It's that simple and I think our fans understand that.
"Having said that, if Craig were to take a view that he wants to play football at a huge club where he enjoyed himself in the past, and he was willing to take a pay cut then, who knows?
"Manchester City would also have to take a view that it would be in their interests to pay a portion of his wages as well."
Lawwell also expressed his satisfaction with Celtic's latest financial figures, after it was revealed they had slashed their debt by ?8.5million in the last six months to just over ?500,000.
Lawwell added: "We're delighted with how we've managed to reduce the bank debt.
"We've been helped in that respect by players leaving but we have also made ?10.3million available for the manager so overall they really are a very decent set of results."
Source: Team Talk
Source: Team Talk